Does “this sentence is false” defeat a self-referential universe?
The liar combines self-reference with an unrestricted truth assignment: declaring the sentence true makes it false, and declaring it false makes it true. It shows that those demands cannot all be imposed together in the ordinary two-valued way. It does not show that every self-reference is inconsistent. An equation can refer to its own unknown and have a perfectly definite solution. OPH requires a specified domain, maps and admissible comparisons; a proposed closure with contradictory requirements fails rather than becoming a physical universe. Its fixed-point proposal therefore does not assume that every self-referential description has a solution. Logical approaches to truth still need their own rules; an observer network does not erase the liar by agreement.
See also What about the set of all sets that do not contain themselves? (Russell’s paradox), Can everything true be proven?, Can reality contradict itself?
Sources: The liar paradox
Also in Chapter 6: Why Isn't Agreeing With Your Neighbors Enough?, Chapter 37: Why Does the Loop Have No Beginning?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 2: Why Is There Anything Rather Than Nothing?watch a universe make its own particles